SimpleMKKM improves multi-kernel clustering efficiency.
problem Efficient multi-kernel clustering.
method Re-formulated minimization-maximization problem into a smooth minimization, solved with gradient descent.
result Outperforms state-of-the-art multi-kernel clustering alternatives.
Proposes a method to select diverse kernels for improved clustering performance.
problem Redundancy in selected kernels degrades clustering performance and efficiency.
method Selects diverse subset of kernels as representative kernels, optimizes combination coefficients using alternating minimization.
result Improves clustering performance and efficiency compared to existing methods.
Study provides guarantees for kernel clustering under non-parametric mixtures.
problem Statistical guarantees for kernel-based clustering without strong assumptions.
method Non-parametric mixture models, kernel-based clustering, consistency guarantees.
result Necessary and sufficient separability conditions for consistent clustering recovery.
Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.
problem Large memory usage in kernel-based clustering for large-scale datasets.
method Approximate the kernel matrix using incomplete Cholesky factorization and apply linear k-means clustering. result The proposed method achieves similar performance to kernel k-means clustering but handles large-scale datasets efficiently. Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
Paper improves clustering risk bounds for kernel k-means.
problem Improving clustering risk bounds for kernel k-means.
method Analyzes kernel k-means and Nyström approximation.
result Achieves nearly optimal excess clustering risk bound.
Improved kernel k-means clustering for large datasets with reduced computational cost.
problem High computational cost of kernel k-means clustering for large datasets.
method Applying linear k-means clustering to a subset of features constructed using rank-restricted Nyström approximation.
result Achieves a 1+ε approximation ratio for kernel k-means cost function.
Paper studies robustness of kernel clustering methods.
problem Robustness of kernel clustering methods.
method Semidefinite programming relaxation for kernel clustering problem.
result SDP is strongly consistent and achieves exact recovery, K-SVD is weakly consistent.
A new distributed clustering framework using distributional kernel.
problem Clustering in distributed networks with arbitrary shapes, sizes, and densities.
method Distributed Clustering based on Distributional Kernel (KDC) using similarity of distributions.
result KDC guarantees equivalent clustering outcomes to centralized methods, reduces runtime, and discovers arbitrary clusters.
Adaptive clustering uses kernel density estimates for split detection.
problem Cluster detection in non-parametric settings.
method Recursive algorithm using kernel density estimates for splitting and clustering.
result Finite sample guarantees, consistency, and adaptive bandwidth selection.
Unified kernel approach for similarity and clustering.
problem Challenges in similarity measurement and nonlinear similarity.
method Simultaneously learns cluster indicator matrix and similarity information in kernel spaces.
result Automatic optimization of cluster indicator matrix, similarity relations, and kernel combination.
Kernel clustering methods have biases due to density, which can be corrected.
problem Density biases in kernel clustering methods.
method Theoretical analysis and proposed solutions to density biases.
result Density biases can be corrected by density equalization using locally adaptive weights or kernels.
Kernel K-means clusters probability distributions.
problem Clustering a sample of probability distributions.
method Mapping distributions to kernel mean embeddings in RKHS, then applying K-means.
result Effective unsupervised classification of probability distributions.
New clustering method using point-set kernel measures similarity.
problem Measuring similarity between objects for clustering.
method Point-set kernel for similarity computation; clustering procedure uses this measure.
result Proposed method is more effective and faster than existing algorithms.
KT combines treelets with kernel functions for hierarchical clustering.
problem Hierarchical clustering of non-numeric data.
method Combines treelets and kernel functions to handle non-numeric data.
result KT effectively clusters non-numeric data.
Paper studies kernel hyperparameters for clustering, proposing an efficient search method.
problem Challenges in tuning kernel parameters for clustering, especially for RBF kernels.
method Derives a lower bound for RBF kernel parameters, proposes an efficient hyperparameter search algorithm.
result Proposes an efficient algorithm for hyperparameter search in kernel clustering, improving upon grid search.
ABC learns context-aware representations for clustering.
problem Learning latent representations that adapt to context in machine learning.
method Attention-based neural architecture that learns a similarity kernel.
result Competitive results for clustering Omniglot characters.
The paper examines the optimality of kernel methods in high-dimensional clustering.
problem Understanding the optimality of kernel methods in high-dimensional data clustering.
method High-dimensional Gaussian clustering, exponential kernel function, kernel k-means, semi-definite relaxation.
result The exponential kernel function optimally recovers clusters in high-dimensional data, matching information-theoretic limits up to a factor of √2.
Proposes rpf-kernel for clustering via random projection forests.
problem Clustering similar data points while distinguishing them from dissimilar ones.
method Random projection forests to learn a similarity kernel.
result rpf-kernel effectively clusters data with competitive performance.
PCKID kernel improves spectral clustering on incomplete data.
problem Handling incomplete data in spectral clustering.
method Combining posterior distributions of Gaussian Mixture Models on different scales.
result PCKID kernel outperforms baseline methods for all fractions of missing values.
Kernelized convex clustering handles non-linear and non-convex data.
problem Lack of effective clustering methods for non-linear and non-convex data.
method Kernelized convex clustering in RKHS.
result Superior performance compared to state-of-the-art techniques.
DKLM learns adaptive kernels for robust nonlinear subspace clustering.
problem Nonlinear structures in data and challenges with kernel-based clustering.
method Data-driven kernel learning with adaptive weighting and optimal block-diagonal affinity matrix.
result DKLM enhances robustness and preserves manifold structure in nonlinear space.
Proposes a method to learn a low-rank kernel matrix for graph-based clustering.
problem Challenges in learning an optimal kernel matrix for graph-based clustering.
method Unified framework for graph construction and kernel learning, focusing on a low-rank kernel matrix.
result Efficacy of the proposed method validated through extensive experiments.
Corrects proofs for kernel-k-means clustering validity.
problem Ensuring the existence of kernel functions for k-means clustering. method Revises Gower's proofs and addresses missing conditions.
result Establishes the existence of kernel functions for k-means. A new randomized method reduces memory usage for kernel clustering.
problem High memory usage in kernel-based clustering methods.
method Randomized approximation followed by standard K-means.
result Significantly less memory usage compared to standard methods.
t-SNE with Cauchy kernel shows finer cluster structure.
problem Crowding problem in t-SNE visualizations.
method Developed an efficient implementation of t-SNE with a heavy-tailed t-distribution kernel. result Fine cluster structure revealed with ν<1. Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
problem Learning a tree end-to-end for clustering without labels is an open challenge.
method Greedy maximization of the kernel KMeans objective without centroids.
result Kauri often outperforms existing unsupervised clustering methods, especially with non-linear kernels.
Proposes a method to preserve graph similarities for better clustering accuracy.
problem Sub-optimal performance due to non-similarity-preserving kernels in graph-based clustering.
method Adaptive graph learning method that preserves pairwise similarities and unifies clustering and graph learning.
result Improves clustering accuracy by preserving pairwise similarities in the graph.
New algorithm clusters data and learns kernels without relaxing constraints.
problem Learning kernels or distance metrics from pairwise constraints without losing generalization.
method Joint clustering and kernel learning without relaxing constraints.
result Outperforms existing approaches on diverse datasets.
Deep kernel learning for clustering improves on spectral methods.
problem Discovering effective kernels for clustering.
method Neural network producing embeddings motivated by spectral clustering, optimized via gradient adaptations on the Stiefel manifold.
result Trained embeddings outperform state-of-the-art deep clustering methods and traditional approaches.
Kernel methods summarize and integrate posterior similarity matrices from Bayesian clustering.
problem Summarizing and integrating posterior similarity matrices from Bayesian clustering.
method Positive semi-definite PSMs, kernel matrices, kernel methods, combining kernels.
result Kernel methods effectively summarize and integrate posterior similarity matrices.
In this thesis, we propose several modelling strategies to tackle evolving data in different contexts. In the framework of static clustering, we start by introducing a soft kernel spectral clustering (SKSC) algorithm, which can better deal with overlapping clusters with respect to kernel spectral clustering (KSC) and p…
Proposes a novel method to cluster individuals based on treatment effects.
problem Identifying subpopulations with different treatment responses.
method Clusters individuals using a learned kernel derived from causal forests, revealing latent subgroup structures.
result Captures meaningful treatment effect heterogeneity through kernelized clustering.
Study spectral properties of radial kernels for high-dimensional mixtures.
problem Understanding spectral properties of radial kernels for high-dimensional mixtures.
method High-dimensional analysis focusing on concentration properties of components in mixtures.
result Kernel PCA can successfully cluster mixtures with common means but different covariances, even in high dimensions.
This paper clusters networks with annotated time-series data using kernel-ARMA and Grassmannian geometry.
problem Clustering networks with annotated time-series data, including state, node, and subnetwork clustering.
method Extract features from time-series data using kernel-ARMA, map onto Grassmannian, and cluster using Riemannian geometry.
result The proposed framework outperforms state-of-the-art clustering schemes on brain-network data.
We propose a new method to model multi-way similarities into hypergraphs for clustering.
problem Clustering real-valued data using hypergraphs with multi-way similarities.
method Formulate multi-way similarities using kernel functions, establish connections to hypergraph cut, and develop a fast spectral clustering algorithm.
result Our method outperforms existing graph and heuristic modeling methods in clustering performance.
Paper proposes a new framework for learning discriminative similarity for clustering and semi-supervised learning.
problem The importance of pairwise similarity for clustering and semi-supervised learning performance.
method Proposes a novel discriminative similarity learning framework that learns from hypothetical labelings and minimizes generalization error.
result Discriminative similarity learned from hypothetical labelings can improve clustering and semi-supervised learning performance.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in th…
Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In this paper we define a general class of kernels that can be easily approximated …
A new MKL framework improves graph-based clustering and semi-supervised classification.
problem MKL methods often fail to improve performance over single kernels.
method Proposes a new MKL framework based on consensus kernels and automatic weight assignment.
result The proposed method outperforms existing MKL methods on multiple benchmark datasets.
Paper proves MS convergence for radially symmetric kernels with large bandwidths.
problem Proving convergence of mean shift algorithm with radially symmetric kernels.
method Analyzes convergence of mean shift algorithm with radially symmetric, positive definite kernels.
result Guaranteed convergence for sufficiently large bandwidth in any dimension.
Quantum SVM clustering speeds up big data analysis.
problem Performance degradation of classical SVM clustering on big data.
method Developed a quantum version of SVM clustering using quantum support vector machine and kernels.
result Significant speed-up gain on run-time complexity.
KLIC combines multiple datasets for clustering, down-weighting noisy data.
problem Robustness of COCA in noisy or conflicting datasets.
method Multiple Kernel Learning for Integrative Clustering.
result KLIC down-weights noisy datasets, improving clustering accuracy.
Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping clusters on a high feature space using mercer kernel techniques to improve separa…
Flexible band grouping and kernel fusion for hyperspectral image processing.
problem Large dimensionality in hyperspectral imaging.
method Non-contiguous and contiguous band grouping for dimensionality reduction; improved visual clustering; unsupervised clustering algorithms; diverse features via different proximity metrics and kernel functions; l∞-norm multiple kernel learning. result Heterogeneous features and kernels lead to performance gain.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
An algorithm learns a kernel matrix from relative-distance constraints for semi-supervised clustering.
problem Learning metrics from relative-distance constraints to capture finer structures.
method Log determinant divergence for kernel matrix learning with relative-distance constraints.
result Kernels learned from relative-distance constraints yield better clusterings than existing methods.